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%	DOCUMENT INFORMATION
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\title{\textbf{Local consistencies for binary contraints}} % Title

\author{KHONG Minh Thanh} % Author name

%\date{\today} % Date for the report

\begin{document}

\maketitle % Insert the title, author and date

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%Date Performed: & January 1, 2014 \\ % Date the experiment was performed
%Partners: & KHONG Minh Thanh \\ % Partner names
%Instructor: & Professor Yves % Instructor/supervisor
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%	SECTION 1
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\section{Local consistencies for binary constraints}
\textit{\textbf{Some general definitions:}}
	\begin{itemize}
	\item \textit{(i,j)-Consistency}
		\begin{itemize}
		\item[+] has non-empty domain
		\item[+] any consistent assigment of $i$ variables can be extended to a consistent assigment involving $j$ addition variables
		\end{itemize}
	\item \textit{Strong (i,j)-Consistency}
		\begin{itemize}
		\item[+] is $(k,j)$ consistent for all $k \leq i$
		\end{itemize}
	\item \textit{Path Consistency (2-Path Consistency)}
		\begin{itemize}
		\item[+] is $(2,1)$-consistent
		\end{itemize}
	\item \textit{Strong Path Consistency}
		\begin{itemize}
		\item[+] is \textbf{strong} $(2,1)$-consistent
		\end{itemize}
	\item \textit{m-Consistency}
		\begin{itemize}
		\item[+] is (m-1,1)-consistent
		\end{itemize}
	\item \textit{Strong m-Consistency}
		\begin{itemize}
		\item[+] is \textbf{strong} (m-1,1)-consistent
		\end{itemize}
	\end{itemize}

\textit{\textbf{Domain filtering consistency:}}
	\begin{itemize}
	\item \textit{Restrict Path Consistency (RPC)}
	\item \textit{Path Inverse Consistency (PIC)}
	\item \textit{Max Restrict Path Consistency (Max-RPC)}
	\item \textit{Neighborhood Inverse Consistency (NIC)}
	\item \textit{Singleton Arc Consistency (SAC)}
	\end{itemize}

\section{Local consistencies for non-binary constraints}
\textit{\textbf{Non Domain-based consistencies}}
	\textit{
	\begin{itemize}
	\item Relational Arc Consistency \textbf{(Rel AC)}
	\item Relational Path Consistency \textbf{(Rel PC)}
	\item Relational m-Consistency
	\item (Strong) Relational (i,m)-Consistency
	\end{itemize}
	\begin{itemize}
	\item Pairwise Consistency \textbf{(PWC)}
	\item k-wise Consistency
	\item Hyper-m-Consistency
	\end{itemize}
	}
\textit{\textbf{Generalized arc consistency (GAC)}}

- Combine \textbf{PWC} with \textbf{GAC} we have: \textbf{PWC + GAC}

\textit{\textbf{Singleton Generalized arc consistency (SGAC)}}

\textit{\textbf{Domain-base consistencies}}

\begin{itemize}
\item \textit{Relational Path Inverse Consistency \textbf{(Rel PIC)}}
\item \textit{Restricted Pairwise Consistency \textbf{(RPWC)}}
\item \textit{Max Restrited Pairwise Consistency \textbf{(Max-RPWC)}}
\end{itemize}






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